Antenna Paradox

[k4kyv]

I always thought I understood perfectly the theory behind zepp type antennas fed with open wire tuned feeders, but an example I found in an article in August 1934 R/9 magazine has left me in somewhat of a conundrum.

See Figures 1 and 2 in the attachment. If a 250 foot length of wire is stretched out straight it is approximately one wavelength long for the amateur 80m band.  Now if it is bent as in Fig.1 it is still one wavelength long, but only the first and last quarter are radiating.  It has become a bent antenna, but still tunes the same ways as before, that is, it resonates at 80m or thereabouts.  If we cut the wire into two pieces precisely at the mid point as in Fig. 2 we have two pieces of wire, each 125 ft. long.  This becomes the familiar half-wave dipole fed with a quarter wavelength open wire feed line.

In Fig. 2 we find voltage maximum points and current minimum points at each end of each one of our 125 ft. pieces of wire.  We can feed the antenna as a half-wave dipole, using a parallel tuned circuit connected to the other end of the open wire feedline.

But what about Fig. 1?  If the 250-foot piece of wire is stretched out straight, we can end feed it as a 1-wavelength antenna with no problem, using a tuner that will match the high impedance at the voltage-maximum feed point, or we could feed it end-fed zepp fashion.  It follows that if we bend the wire as in Fig. 1 it will still resonate as a 1-wavelength wire and we can still feed it at one end, but only the first and last quarter will radiate. The feed point impedance will be altered but still high, so it should be only a matter of re-adjusting our matching network to accommodate the new impedance.

But we know that a half wave dipole exhibits approximately a 75-ohm impedance at the midpoint.  We also know that a quarter wave stub, shorted at one end as in Fig. 1 will exhibit a very high impedance at the opposite end.  This quarter-wave stub will appear essentially as an open circuit where it feeds at the midpoint of the dipole and will isolate the two halves of the dipole from each other, so each end of the antenna should exhibit a low impedance to ground, each half of the dipole becoming an independent quarter-wave antenna.  OTOH, the whole thing is still a full-wave resonant piece of wire, so each end should exhibit a high impedance to ground at the resonant frequency.

[W2DU]

Don, I believe I can help in solving the antenna paradox.

First, Fig 2 shows a normal half-wave dipole, center fed with open-wire line (of any length).

Now let's voltage feed the antenna in Fig 1 from either end. Consider the junction points where the 1/4wl section joins the flat top. Let's call the right-hand junction point A and the left-hand junction point B.

Let current entering from the right-hand end of the flat top arrive at point A as (+). The current now enters the 1/4 wl section, which has a total length of 1/2 wl, or 180°. Therefore, during the half-wavelength of time the current flows through the 1/4 wl section the current at point A has reversed in polarity to (-). Consequently, with the current at point B at (+) and the current at point A at (-), we have two 1/4 wl sections of flat top operating as if it were fed in the center by the shorted 1/4 wl section. It's as if the source generator were placed between the two 1/4 wl flat-top sections, the same as in Fig 2.

The radiation characteristics of both Figs 1 and 2 are therefore identical, even though the radiator of Fig 1 is fed at the end (voltage point), while the radiator of Fig 2 is fed in the center (current point).

I'm not sure that my explanation is worded as well as I'd like, but I hope the concept comes through.

Walt

[k4kyv]

Walt,

I thought about that too, but the problem I see is that (Fig. 1) at the shorted end of the 1/4λ section, the high voltage appearing at the end of each feeder is bound to be in phase with the other, since the two are tied together at the high voltage point.  If you unshort the section (Fig. 2) and feed the transmission line with a parallel tuned circuit such as a balanced link coupled tuner, the two feeders are excited 180° out of phase with each other since the parallel tuned circuit is inserted between the feeders and it introduces a phase reversal.  Therefore, the high voltage appearing at the end of each feeder is out of phase with the other.

[W2DU]

Don, in this situation one must follow the money--oops, I mean current. When fed at the end, as I said before, the right-hand end, then let the current at point A be (+). The current then flows through the 1/4wl section, taking 180° in time. When the current reaches point B the current at point A has reversed (-). Thus the currents and voltages at points A and B are out of phase, as they should be when fed at the center of a dipole. For there to be high voltage on both sides of the shorting-bar location in the 1/4wl stub simultaneously the flat top would have to fed from both ends simuntaneously.

The 1/4wl stub of Fig 1 is used to feed two collinear half wavelength dipoles in phase, or even three, or four 1/2wl dipoles in phase, so as to reverse the phase at what would otherwise be a direct junction of all the collinear dipoles. This concept is shown very clearly in the ARRL Handbook. For example, let's take a 1 lambda-length radiator fed at the end--it's two half waves out of phase, because at the center there is no change in phase. However, inserting the 1/4wl shorted stub causes a phase change at the center, as between points A and B in your Fig 1. This phase change occurs because the current flowing though the 1/4wl stub requires 180° in time to traverse the stub.

Hope this helps.

Walt

[W2DU]

Don, I made a mistake--I made reference to the ARRL Handbook, when I should have said the ARRL Antenna Book.

On the assumption that you may not have the Antenna Book I scanned the appropriate page in PDF and am attaching it. I'm sure this page will help.

Walt

[kb3ouk]

I have a question about the 4 element collinear array. would someone be able to take a similar array and have the elements and matching stubs tuned for 40 meters, then make a switching system that would connect the stubs (by having a pair of switches across the stubs that would open up when switched for 40 meters) into the antenna when used on 40 meters, and use the whole length as a 4 element array, then on 80 meters open the antenna ahead of the stubs by using another set of switches and using the antenna as a regular dipole, then on 160 shut all the switches (and shorting the stubs) and have another dipole. just a thought, i" curious if this would even work.
Shelby KB3OUK

[Steve - WB3HUZ]

No need for the switches. The stubs will only produce the phase shift/reversal on 40 meters. On the lower bands, they would act more like linear loading sections, making the antenna "look" longer. The patterns on the lower bands would approximate a dipole, especially on 160 meters.

[W2DU]

I've been muddling over what I've said in my earlier posts on this thread. I may have painted myself into a corner, so I'm still workin' on it.

Where I've probably gone wrong is in having the 1/4wl stub in the center of Don's 1 wl radiator in his Fig 1. This configuration has placed the stub in the center of two 1/4wl sections, in the center of two 1/2wl sections, as in the collinear half waves in phase.

With the 1/4wl shorted stub section in the center of two 1/4wl radiators the currents in the radiators are reversed in direction, where the currents are not reversed without the stub section. Without the stub section the current is in phase all along the half-wave radiator.

I've got to do more thinking to get myself out of the corner. Stay tuned, I'll be back.

Walt

[W2DU]

I previously said that both of Don's Figs 1 and 2 would have the same radiation characteristics. And I presented some chatter that I thought proved it.

I was wrong! So please allow me to climb out of the corner I painted myself into.

First, Don's Fig 1 amounts to two 1/4wl segments of a radiator connected with a 1/4wl shorted phase-inverting stub, thus the two 1/4wl segment do NOT make a half-wave dipole.

So let me start over again from a slightly different approach.

In a half-wave dipole the current flows in the same direction throughout its length, and we know the radiation pattern is a single broad lobe broadside to the dipole.

In a full-wave radiator (no longer a dipole) the current flows in opposite directions in each half-wave section, because at the center of the radiator the direction of the current reverses. Thus the full-wave radiator consists of two half-waves OUT OF PHASE. The resulting radiation pattern is two lobes radiating at +45 and -45°, respectively, with a null broadside.

Now we come to the difference between the full-wave radiator and two half-waves in phase. Since the currents flow in opposite directions in the half-waves of the full-wave radiator, to bring the two half-waves IN PHASE. we must make the currents in the two half-waves to flow in the same direction. Thus, to make the currents in the full-wave radiator flow in the same direction in both half-wave sections, we insert a 1/4wl shorted-stub phase inverter at the center of the full-wave radiator. The resulting radiation pattern is single lobe broadside, but with a narrower lobe than that produced by a single half-wave radiator.

Since the currents in the two half-wave sections in the full-wave radiator flow in opposite directions, producing two lobes and a null broadside, it also follows that if currents in two quarter-wave sections are flowing in opposite directions, the radiation pattern from this combination should also produce two lobes with a null broadside. This is the combination shown in Don's Fig 1, two 1/4wl sections connected together with the 1/4wl shorted stub (phase inverter), causing the currents in the two sections to flow in opposite directions, in other words, causing the two 1/4wl flat-top sections be out of phase.

Consequently, I was wrong earlier when I stated that the radiation characteristics of both of Don's Figs 1 and 2 are identical. They are radically different, as I have explained above.

I have consequently taken ten lashes with a wet noodle for my error. Sorry folks.

Walt

[kb3ouk]

As I remember seeing it in a book once, for every half wavelength of an antenna, there should be two lobes. The fullwave antenna would have a pattern similar to a four leaf clover, because of being out of phase, which makes me think that the two lobes per half wave of wire is mainly for out of phase antennas, right? What I wonder is why a full wave wire fed at the end also radiates in the same cloverleaf pattern as centerfed out of phase fullwave wire. There's probably something that I'm not catching on to.

[Steve - WB3HUZ]

But if you feed Figure 1 from one end and Figure 2 from the middle, the radiation patterns will be identical.

[k4kyv]

I think I have figured it out, and it looks like Walt did too.

See attachment.  Fig. 3A shows a full wavelength wire excited with rf at one end.  Note the polarity of the high voltage points at A, C and E, and the voltage nulls at B and D. Assume the wire is excited at one end. As Walt said, we have a clover-leaf pattern with lobes at 45° points, and nulls broadside and off each end.

Fig. 3B shows the same full wavelength piece of wire split at the mid point, and a parallel tuned circuit inserted.  The wire could be excited at one end, or by using a coupling link wound over the coil in the tuned circuit.  The parallel tuned circuit inverts the phase at the midpoint of the wire. We now have two halfwaves in phase with the broadside radiation pattern as shown in the diagram.

Now we fold the wires as shown in Fig. 4A and 4B.  

In Fig. 4A, notice that the polarity of the voltage at either end of the antenna is the same.  The polarity of the voltage at the bottom end of the stub (point C) is the same in both wires, and opposite that of the ends of the antenna (points A and E).  This is exactly the same thing as the old-style quarter-wave vertical Tee antenna, shown in Fig. 5A.  In both cases, most of the radiation from the horizontal wire is cancelled.  The primary source of radiation is the stub in 4A and the vertical wire in 5A.  Assuming a good ground in Fig 5A, we have a vertically polarised antenna, in which the horizontal wire serves as a capacity hat that elevates the current loop to the top of the vertical wire.

In 4B, the full wavelength wire is split at the midpoint, and we excite the antenna via the parallel tuned circuit inserted at point C.  In this case we have a simple half wave dipole antenna fed with a quarter-wave resonant transmission line. The voltages at the ends of each of the the two wires in the transmission line at point C are opposite in polarity, and the radiation pattern is broadside to the wire.  This is identical to the coax-fed dipole shown below, in Fig. 5B.

In Fig 4A, the stub does most of the radiation, not the horizontal wire.  If we have a good ground plane beneath the antenna, it should radiate with good efficiency.  Without a ground plane, the antenna at 4A is like many of the commercial "no-radials-needed" ham verticals; most of the rf is lost warming the earth below.

[W2DU]

Don, I agree with your additional diagrams, but you haven't told us how Fig 4A is fed.

And Steve, Don's Fig 1 and Fig 4A show the same configuration of the radiators. Consequently, if his Fig 1 is fed from an end and Fig 2 fed in the center, their radiation patterns cannot be identical.

Walt

[k4kyv]

Don, I agree with your additional diagrams, but you haven't told us how Fig 4A is fed.

At one end, using zepp feeders or a parallel tuned circuit.  Fig. 3A would be fed the same way.   3B could be fed at one end, or by adding a coupling link to the coil in the tuned circuit as in 4B. I omitted the feeder circuitry from the diagrams for clarity and (I had hoped) to avoid  confusion.

4A could also be fed at the bottom (point c) just like the vertical tee in Fig. 5A.
A similar idea is often used in actual practice on 160m, by tying together the parallel feeders or the conductors on the coax feedline of an 80m dipole, and working the whole thing against ground.